Engineering topics

Truong, T. K.

Publications and source records attributed to Truong, T. K..

At least 73 records · Page 4

NASA NTRS1983

New syndrome decoder for (n, 1) convolutional codes

The letter presents a new syndrome decoding algorithm for the (n, 1) convolutional codes (CC) that is different and simpler than the previous syndrome decoding algorithm of Schalkwijk and Vinck. The new technique uses the general solution of the polynomial linear Diophantine equation for the error polynomial vector E(D). A recursive, Viterbi-like, algorithm is developed to find the minimum weight error vector E(D). An example is given for the binary nonsystematic (2, 1) CC.

Reed, I. S.↗

NASA NTRS1983

A parallel-pipeline architecture of the fast polynomial transform for computing a two-dimensional cyclic convolution

It is pointed out that the two-dimensional cyclic convolution is a useful tool for many two-dimensional digital signal processing applications. Two important applications are related to spaceborne high-resolution synthetic aperture radar (SAR) processing and image processing. Nussbaumer and Quandalle (1978) showed that a radix-2 polynomial transform analogous to the conventional radix-2 FFT algorithm can be used to compute a two-dimensional cyclic convolution. On the basis of results reported by Arambepola and Rayner (1979), a radix-2 polynomial transform can be defined to compute a multidimensional cyclic convolution. Truong et al. (1981) used the considered ideas together with the Chinese Theorem to further reduce the complexity of the radix-2 fast polynomial transform (FPT). Reed et al. (1981) demonstrated that such a new FPT algorithm is significantly faster than the FFT algorithm for computing a two-dimensional convolution. In the present investigation, a parallel-pipeline architecture is considered for implementing the FPT developed by Truong et al.

Truong, T. K.↗

NASA NTRS1982

The VLSI design of a single chip Reed-Solomon encoder

A design for a single chip implementation of a Reed-Solomon encoder is presented. The architecture that leads to this single VLSI chip design makes use of a bit serial finite field multiplication algorithm.

Truong, T. K.↗

NASA NTRS1982

A parallel VLSI architecture for a digital filter of arbitrary length using Fermat number transforms

A parallel architecture for computation of the linear convolution of two sequences of arbitrary lengths using the Fermat number transform (FNT) is described. In particular a pipeline structure is designed to compute a 128-point FNT. In this FNT, only additions and bit rotations are required. A standard barrel shifter circuit is modified so that it performs the required bit rotation operation. The overlap-save method is generalized for the FNT to compute a linear convolution of arbitrary length. A parallel architecture is developed to realize this type of overlap-save method using one FNT and several inverse FNTs of 128 points. The generalized overlap save method alleviates the usual dynamic range limitation in FNTs of long transform lengths. Its architecture is regular, simple, and expandable, and therefore naturally suitable for VLSI implementation.

Truong, T. K.↗

NASA NTRS1982

The VLSI design of a Reed-Solomon encoder using Berlekamps bit-serial multiplier algorithm

Realization of a bit-serial multiplication algorithm for the encoding of Reed-Solomon (RS) codes on a single VLSI chip using NMOS technology is demonstrated to be feasible. A dual basis (255, 223) over a Galois field is used. The conventional RS encoder for long codes ofter requires look-up tables to perform the multiplication of two field elements. Berlekamp's algorithm requires only shifting and exclusive-OR operations.

Truong, T. K.↗

NASA NTRS1981

Digital SAR processing using a fast polynomial transform

A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network.

Butman, S.↗

NASA NTRS1981

A new CT collimator for producing two simultaneous overlapping slices from one scan

A new CT collimator is developed which is capable of producing two simultaneous successive overlapping images from a single scan. The collimator represents a modification of the standard EMI 5005 collimator achieved by alternately masking one end or portions of both ends of the X-ray detectors at a 13-mm beamwidth so that a set of 540 filtered projections is obtained for each scan which can be separated into two sets of interleaved projections corresponding to views 3 mm apart. Tests have demonstrated that the quality of the images produced from these two projections almost equals the quality of those produced by the standard collimator from two separate scans. The new collimator may thus be used to achieve a speed improvement in the generation of overlapping sections as well as a reduction in X-ray dosage.

Kwoh, Y. S.↗

NASA NTRS1981

Addendum to 'A new hybrid algorithm for computing a fast discrete Fourier transform'

The reported investigation represents a continuation of a study conducted by Reed and Truong (1979), who proposed a hybrid algorithm for computing the discrete Fourier transform (DFT). The proposed technique employs a Winograd-type algorithm in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. The implementation of the technique involves a considerable number of additions. The new investigation shows an approach which can reduce the number of additions significantly. It is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm.

Reed, I. S.↗

NASA NTRS1981

A decoding failure test for the transform decoder of Reed-Solomon code

Using a finite field transform, a transform decoding algorithm is able to correct erasures as well as errors of any (n,k,d) Reed-Solomon code over the finite field GF(q). A pitfall of transform decoding and how to avoid it are discussed. A simple test is given so that the decoder fails to decode instead of introducing additional errors, whenever the received word contains too many errors and erasures.

Miller, R. L.↗

NASA NTRS1981

Fast polynomial transform and its implementation by computer

A fast polynomial transform (FPT) algorithm for computing two-dimensional cyclic convolutions on a general-purpose computer is demonstrated and compared with the FFT approach. An FPT program for two-dimensional convolutions written in FORTRAN is shown to be 20% faster than the conventional FFT algorithm. This higher speed advantage makes the FPT algorithm a candidate for many two-dimensional digital image filtering applications.

Reed, I. S.↗

NASA NTRS1981

Fast transforms for decoding Reed-Solomon codes

In the paper it is shown that the Chinese remainder theorem when coupled with a modification of Winograd's method can be used to compute Fourier-like transforms over GF (s super m), where m = 2, 3, . . . , 8. These new transform techniques are to decode Reed-Solomon codes of block length 2 super m -1. The results are shown to be more efficient than the more conventional method.

Reed, I. S.↗

NASA NTRS1980

A bandpass filter for the enhancement of an X-ray reconstruction of the tissue in the spinal canal

In this communication, a new bandpass reconstruction filter is developed to partially remove the low spatial frequencies of the bone and the soft tissue in an X-ray reconstruction of a lumbar spine. This partial removal of the low frequencies suppresses the bony vertebral body and the soft tissue components within the projections of actual clinical data. It also has the effect of enhancing the sharp edges of the fatty tissue surrounding the spinal cord region. The intent of this effort is to directly visualize the spinal cord without the need for water-soluble contrast (e.g., metrizamide) to be installed through lumbar punctures.

Reed, I. S.↗

NASA NTRS1980

Concerning the feasibility of a real time SAR digital processor for VOIR low resolution imaging modes

The feasibility of real time digital processing of synthetic aperture radar data for Venus orbiting imaging radar low resolution modes was investigated. First, it is shown that range migration is not a problem for these modes. Then, under the assumption of no range migration, fast Fourier transform implementations for accomplishing both range and azimuth correlation in real time are shown to be feasible with current technology.

Truong, T. K.↗

NASA NTRS1980

Efficient program for decoding the /255, 223/ Reed-Solomon code over GF/2 to the 8th/ with both errors and erasures, using transform decoding

The paper deals with a method developed for decoding a (255, 223) Reed-Solomon code over GF(2 to the 8th) with both errors and erasures. The matrix of decoding times for correcting errors and erasures of the code using a simplified decoder is presented. It is shown that the algorithm proposed is faster by a factor of from three to seven.

Miller, R. L.↗

NASA NTRS1980

On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution

A fast algorithm is developed to compute two dimensional convolutions of an array of d sub 1 X d sub 2 complex number points, where d sub 2 = 2(M) and d sub 1 = 2(m-r+) for some 1 or = r or = m. This algorithm requires fewer multiplications and about the same number of additions as the conventional fast fourier transform method for computing the two dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.

Truong, T. K.↗

NASA NTRS1980

Wiener filtering of successive overlapping sections of an X-ray reconstruction

In this paper, a technique is developed to improve the image quality of an object in three-dimensional reconstruction by a weighted average of successive overlapping two-dimensional sections of the object. It is demonstrated that the signal-to-noise ratio of a two-dimensional picture can be improved by roughly a factor of 2 for typical X-ray beam shapes.

Reed, I. S.↗

NASA NTRS1979

Simplified algorithm for correcting both errors and erasures of Reed-Solomon codes

Using a finite-field transform, a simplified algorithm for decoding Reed-Solomon codes is developed to correct erasures as well as errors over the finite-field GF(q to the m power), where q is a prime and m is an integer. If the finite-field transform is a fast transform, this decoder can be faster and simpler than a decoder that uses more conventional methods.

Reed, I. S.↗

NASA NTRS1979

Decoding of B.C.H. and R.S. codes with errors and erasures using continued fractions

Through the use of continuing fractions, a simplified algorithm for decoding B.C.H. and R.S. codes is developed that corrects both erasures and errors on a finite field GF(q to the m). It is noted that the decoding method is a modification of the Forney-Belekamp technique. Finally, it is believed that the present scheme is both simpler to understand and to implement than more conventional algorithms.

Reed, I. S.↗